1. Field of the Invention
The present invention relates to an apparatus for determining the capacitance of a dielectric medium.
2. State of the Art
The on-line and real-time measurement of the biomass content of fermentations is still an active area of research. New sensors are continuously being developed and the already established technologies are constantly being improved. The reason for this need for innovation is that the fermentation industry works with a very broad range of cell types using a very wide range of culturing conditions and under an ever-growing blanket of regulatory requirements.
To fit easily into an already-established fermentation installation, a biomass monitoring system must be generic and capable of working via the currently available probe ports, must not pose a significant contamination risk, be capable of withstanding in-situ the high temperatures and pressures or caustic nature of sterilisation processes, and the probe materials must be inert. The equipment must be supplied in a form that can easily be incorporated into (and survive in) a fermentation hall environment. This is true before any consideration can be given to its ability to work with the cell system being monitored.
The fermentation broth itself is a particularly hostile environment for any sensor to work in. The growth of the cells and the feeding and control regimes used ensure that it is an ever changing environment. The presence of vigorous and fluctuating aeration, and time-dependent temperature profiles, are a particular problem. The medium used can be highly viscous and often contains a wide range of non-biomass solids and immiscible liquids, particularly at the start of the fermentation. The medium""s constitution can change markedly as the cells grow and consume its components.
An ideal measuring system should be capable of working with a wide variety of cell types, ranging from bacterial cells and yeasts, through filamentous fungi and bacteria to animal and plant cells, in both free and immobilised forms. The ability to measure a wide range of biomass concentrations is important, as is the inclusion of an in-situ cleaning system that can remove cellular growth on the sensing probe.
A widening body of literature has demonstrated that the measurement of biomass by use of a capacitive probe provides the best and most generic method in practical situations. Sensor methods based on two-pin electrodes and electromagnetic coupling are being developed but as yet have not been refined enough to work in anything other than laboratory model systems. The most highly developed technology that has found practical utility in industry is the Biomass Monitor (BM). This instrument fulfils the majority of the criteria outlined above and published work has shown it to work well for bacteria, yeast, filamentous fungi and bacteria, animal and plant cells, immobilised cells, for solid substrate fermentations of filamentous fungi, and in assessing cytotoxicity. Its major applications in industry so far have been for controlling the pitching of yeast slurries in brewing and for monitoring microbial fermentations in the pharmaceutical industry.
Details of biological dielectrics and the theory behind capacitive (dielectric) biomass measurements are well known to those skilled in the art. For the purposes of this specification a simplified heuristic model will be described. Cells in a suspension can be regarded as having a three-component structure. Outside and inside the cells is a conducting aqueous ionic medium, the former being the suspension medium the latter the cell cytoplasm. Surrounding the conducting cell core is the thin essentially non-conducting plasma membrane. This means that a cell suspension can be regarded, from an electrical point of view, as a suspension of spherical capacitors containing a conducting matrix surrounded by a conducting suspension medium. To make measurements on this system, an electric field is applied via a set of electrodes. The resulting electrical current paths have two routes through the suspension, either around the cells via the external conductance or through them via the membrane capacitance and internal and external conductances. At low radio-frequencies and below ( less than 0.1 MHz), the cell membrane has a very low admittance, most of the current flows around the cells and, as the membrane capacitance is nearly fully charged, the capacitance of the suspension is very high. The more cells that are present per unit volume, the more spherical capacitors are charged and so the higher is the capacitance of the suspension. The low-frequency capacitance gives a measure of cellular volume fraction. As non-biomass material (including necromass) lacks an intact plasma-membrane, it does not give a significant capacitance contribution. At frequencies above 10 MHz, the membrane capacitance is shorted out, the induced charge held by the membranes is very low and so the capacitance of the suspension approaches that of the water in the suspending medium.
From these arguments, one expects the capacitance of a cell suspension to go from a high low-frequency plateau to a low high-frequency one. This fall in capacitance is called the xcex2-dispersion (FIG. 1). The high-frequency residual capacitance due mainly to water dipoles is called C∞. The height of the low frequency plateau above C∞ is called the capacitance increment xcex94Cxcex2 and its magnitude is proportional to the biomass content of the suspension. The frequency when the fall from xcex94Cxcex2+C∞ to C∞ is half completed is called the critical frequency fc. The steepness with which capacitance falls as frequency increases is described by the Cole-Cole xcex1 value. This has values in the range 0= less than xcex1 less than 1 and is supposed to reflect the distribution of relaxation times in the suspension due to heterogeneity. Shown on FIG. 1 are the curves for xcex1 equals 0 (no distribution of relaxation times) and xcex1 equals 0.2. Increasing xcex1 from 0 does not change xcex94C62, fc or C∞, its major effect on the a equals 0.2 plot shown on the figure is that in the frequency window shown the low-frequency plateau is not achieved.
From these arguments, one can see that to estimate the biomass in a fermentation broth, all that is necessary is to measure the xcex94Cxcex2 of the suspension. On the BM this is done in either of two ways. FIG. 2 line (a) shows a xcex2-dispersion with a spot measuring frequency typically 0.4 MHz) marked by an arrow and the capacitance at that frequency marked by a dot on the curve. As can be seen, the capacitance at the measuring frequency is a good approximation of the xcex94Cxcex2 and hence biomass concentration. In reality, what is done for these single-frequency biomass measurements, and what has been done on this Figure, is to back off the capacitance due to the suspending medium to zero at the spot measuring frequency prior to inoculation. Then any change in the capacitance at that frequency reflect changes in xcex94Cxcex2 and hence biomass concentration. The second capacitive biomass method uses two frequencies, the spot measuring frequency as before and also a high frequency reference (10 MHz). From FIG. 2 it will be seen that the difference in the capacitance between the spot measuring frequency (0.4 MHz) and that at 10 MHz also gives a good estimate of xcex94Cxcex2.
For both methods to work reliably the spot biomass measuring frequency should be well into the low-frequency plateau of the xcex2-dispersion, since the fc of the dispersion can move with changes in the medium conductance. If the measuring frequency were on the falling part of the dispersion, then movements in the fc could cause significant changes in the capacitance measured at the spot frequency and result in corresponding errors in the biomass determination.
To be well onto the plateau means that for most xcex2-dispersions it is necessary to use a measuring frequency below 0.5 MHz. However, this forces the use of a frequency region in which the polarisation of the measuring electrodes can contribute a significant capacitance which interferes with the biomass measurements. This electrode polarisation effect results largely from the charged electrodes attracting around themselves a counter layer of ions which acts electrically as a capacitor/resistor network in series with the biological suspension one is trying to measure.
For a given electrode material, the most important factor that controls the magnitude of this electrode polarisation is the conductance of the suspending medium: the higher the conductance the larger the polarisation, until it completely swamps the xcex2-dispersion. Line (b) on FIG. 2 shows the xcex2-dispersion curve in (a) but with the small amount of polarisation typical of most fermentations. At the spot measuring frequency, the polarisation""s contribution to the signal is quite low and does not result in a significant error in biomass estimation. The real problems occur when the medium conductance is very large and the biomass concentration is comparatively low. This is illustrated by line (c) on FIG. 2, where the xcex2-dispersion line (a) has been swamped by polarisation. Under these conditions, the polarisation results in a large error in the estimated biomass concentration using the spot measuring frequency. Since the magnitude of this polarisation can be time-dependent as the medium conductance changes or as the electrodes become fouled, it is clear that dielectric biomass estimation can be rendered much more difficult.
A variety of methods have been used in the past to remove the electrode polarisation""s contribution to biological capacitance spectra. These include:
(1) Taking measurements with different distances between the measuring electrodes whilst keeping the electrode surface current density constant. As the distance changes, the electrode polarisation""s impedance remains the same whilst the suspension""s impedance changes, enabling the polarisation""s contribution to the signal to be eliminated. This method is impractical for on-line biomass measurements as it involves introducing potentially unreliable moving parts into the fermenter.
(2) Making a frequency scan of the xcex2-dispersion with the electrode polarisation present. Non-linear least squares curve fitting is then used to fit the data to the Cole-Cole equation for the xcex2-dispersion and a term modelling the polarisation. This gives a best estimate value for xcex94Cxcex2 which can be used for biomass estimation. For the BM, the limited frequency range (0.2 to 10 MHz) combined with some residual uncompensated inductances at the higher frequencies means that this method ceases to be reliable under conditions of large polarisation.
(3) The polarisation control method is frequently used for off-line measurements made on the BM. This involves doing a frequency scan of the cell su pension whilst noting down the *conductance at the lowest frequency used. A sample of the suspending medium is then taken and its conductance adjusted, at the lowest frequency, to that of the suspension using distilled water or potassium chloride solution (KCl). A scan of this solution gives an estimate of the polarisation which can subsequently be subtracted from the cell suspension scan to give data largely free from polarisation. This method, however, cannot be put on-line in a fermenter.
(4) Electromagnetically coupled electrodes can eliminate the need for actual physical contact between the metal used in the measuring system and the aqueous ionic suspension medium, thus removing polarisation completely. Although such systems do exist, none of them as yet have been developed enough to be a useful proposition in a real fermentation environment.
(5) Non-polarisable electrodes can be used and indeed the BM used solid pure gold electrode pins. As will be shown later, the recent move to platinum pins for BM probes will result in significant reductions in electrode polarisation. Even platinum, however, does not reduce polarisation enough to allow reliable measurements at very high conductances with a relatively low biomass concentration present.
(6) The BM""s main method of reducing electrode polarisation is the use of a four-electrode pin system. The two outer pins are used to drive current through the sample, whilst the two inner pins are used to detect the potential drop across the suspension that this induces. This potential is detected with a very high impedance voltmeter system which means that virtually no current flows across the inner pins"" electrode/solution interfaces. As it is such a current flow that causes the polarisation, then its elimination also removes the polarisation problem. In reality, the four-terminal electrode configuration works well when compared to say a pair of platinum blacked platinum pins, but it does not remove all the polarisation, especially in highly conducting media.
The BM""s phase detector system is quite capable of accurately detecting quite small capacitance values in the presence of a large conductance. What limits its use, at the high conductances found in animal cell suspensions and in some microbial broths, is the electrode polarisation present. For suspensions with a high biomass content, as in some immobilized systems or high-density cultures, electrode polarisation is not a significant problem even at high conductances. Where a new polarisation elimination method would be useful is in those situations where the xcex2-dispersion curve has become embedded in a large polarisation curve because the biomass concentration is relatively low.
The object of the present invention is to address the above-noted problem.
In accordance with the present invention, there is provided a method for analysing a dielectric medium, said method comprising the steps of measuring, at one or more frequencies, the capacitance between a pair of electrodes immersed in said dielectric medium and determining the proportion of the or each capacitance measurement due to electrode polarisation capacitance and/or to the residual capacitance of the dielectric medium using capacitance measurements made between said electrodes at a first frequency and at a second frequency, the ratio of the respective polarisation capacitances at these two frequencies being pre-determined.
We have established experimentally that capacitance due to electrode polarization is only significant over a frequency range within which the residual capacitance level is substantially constant. Therefore, preferably said first and second measurement frequencies lie within the range over which it is assumed that said residual capacitance level (Cres) is substantially constant.
Assuming the residual capacitance level to be constant, the capacitance measurements made at said first and second measurement frequencies allow this residual capacitance level to be calculated, as well as the respective electrode polarisation capacitances at said first and second measurement frequencies.
The calculated residual capacitance value may be sufficient to establish the biomass content of the dielectric medium. However, we have also established experimentally that a relationship of the form Cpol=Afp exists between electrode polarisation capacitance Cpol and frequency f, where A and p are constants. Therefore, having determined the respective electrode polarisation capacitances at said first and second measurement frequencies, these values may then be substituted into the above equation so that the capacitance due to electrode polarisation may be estimated for any frequency.
Thus, said one or more frequencies may comprise said first and second measurement frequencies. However, said one or more frequencies preferably comprise frequencies other than said first and second frequencies, which other frequencies are preferably greater than said first and second frequencies.
We have further established experimentally that, where the conductance of the dielectric medium exceeds a certain level, the value p is substantially constant for varying conductance.
Thus, the value of p may be estimated using known techniques applied to experimental data obtained for a control medium which preferably comprises a highly conducting, purely aqueous ionic solution. The value p may then be substituted into the above equation to determine appropriate values for said first and second measurement frequencies which provide the required polarisation capacitance ratio.
Alternatively, appropriate values for said first and second measurement frequencies may be determined for the control medium by estimating the polarisation capacitance at a first measurement frequency using known techniques and then varying the measurement frequency to identify the frequency at which the estimated polarisation capacitance has varied by the required amount.
Where p is constant, so too is the ratio between the respective polarisation capacitances at said first and second measurement frequencies. Therefore, an identical polarisation capacitance ratio may be assumed for the same two measurement frequencies at all conductance values exceeding a certain limit, and so appropriate first and second measurement frequencies need only be determined once.
In those circumstances in which the residual capacitance level is not substantially constant, we have found from our experiments that the magnitude of the offset capacitance varies substantially linearly with frequency.
In this case, in order to derive the parameters of the expression representing the relationship between said electrode polarisation capacitance and frequency, preferably one or more additional capacitance measurements are made within the range over which it is assumed that said residual capacitance level varies substantially linearly with frequency.
Also in accordance with the present invention, there is provided an apparatus for measuring, at said one or more frequencies, the capacitance between a pair of electrodes immersed in a dielectric medium and for determining the proportion of the or each capacitance measurement due to electrode polarisation capacitance and/or to the residual capacitance of the dielectric medium using capacitance measurements made between said electrodes at a first frequency and at a second frequency, the ratio of the respective polarisation capacitances at these two frequencies being pre-determined.